The light output of an LED can be highly directional. This directionality has been a detriment when trying to couple LEDs with conventional parabolic reflectors. The directionality of an LED, taken together with the desire to shape the light output in different and sometimes opposite ways to yield a desired performance specification, has resulted in LED lighting systems that frequently employ lens elements in addition to reflectors to shape the beam. These LED-lens-reflector systems can suffer from poor optical efficiency. U.S. Pat. No. 6,318,886 describes a method whereby a beam pattern is produced with LED light sources and a variation of a conventional reflector.